WASHINGTON (AP) -- Resurgent Republicans rallied Sunday behind an agenda based on unwavering opposition to the Obama White House and federal spending, laying the groundwork for gridlock until their 2012 goal: a new president, a "better Senate" and ridding the country of that demonized health care law.

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Republicans said they were willing to work with President Barack Obama but also signaled it would be only on their terms. With control of the White House and the Senate, Democrats showed no sign they were conceding the final two years of Obama's term to Republican lawmakers who claimed the majority in the House.

"I think this week's election was a historic rejection of American liberalism and the Obama and Pelosi agenda," said Rep. Mike Pence, the Indiana Republican who is stepping down from his post in GOP leadership. "The American people are tired of the borrowing, the spending, the bailouts, the takeovers."

Voters on Tuesday punished Democrats from New Hampshire to California, giving Republicans at least 60 new seats in the House. Republicans picked up 10 governorships; the GOP also gained control of 19 state legislative chambers and now holds the highest level of state legislative seats since 1928.

"It was a very rough week, there's no sugarcoating that," said Rep. Chris Van Hollen, D-Md., who led the Democratic Congressional Campaign Committee.

In the days since the election, Speaker Nancy Pelosi, D-Calif., has announced her intention to remain as party leader and has yet to draw any challengers. But a race looms between two veteran members of the leadership for the second-ranking spot in the party.

Rep. James Clyburn of South Carolina, the whip, already has announced his intention to run, and reinforced his decision with a letter Sunday evening asking fellow Democrats for their support.

Rep. Steny Hoyer of Maryland, the current majority leader, has yet to make a formal announcement, but his office on Sunday circulated a letter signed by 30 rank-and-file Democrats endorsing him for the post. They included liberals as well as moderates, but no members of the Congressional Black Caucus, signaling Hoyer is conceding their votes to Clyburn, the highest-ranking African-American in the House.

"I don't see any sign of the president retreating from his principles, but I do see his willingness to reach out, and wherever reasonable and in the interests of moving the economy and jobs forward, he's going to work with the Republicans, as are the Democrats," Van Hollen said.

Republicans have made clear they plan to work stridently against what they view as a White House out of control and out of touch.

"The president did say this week he's willing to work with us," said Rep. Eric Cantor, the Virginia Republican who is in line to become majority leader. "Now listen, are we willing to work with him? First and foremost, we're not going to be willing to work with him on the expansive liberal agenda he's been about."

First target: Democrats' signature health care law.

"This was a huge, huge issue in the election last Tuesday," said Senate Minority Leader Mitch McConnell, R-Ky. "A vast majority of Americans feel very, very uncomfortable with this new bill. People who supported us, political independents, want it repealed and replaced with something else. I think we owe it to them to try."

But the reality remains that Republicans do not have enough seats to marshal through a full repeal if Democrats remain steadfast in their support. Even if Republicans were able to sway enough Democrats to support their effort, it would face a certain veto from Obama.

"Admittedly, it will be difficult with him in the White House," McConnell said. "But if we can put a full repeal on his desk and replace it with the kind of commonsense forms that we were advocating during the debate to reduce spending, we owe it to the American people to do that."

Rep. Paul Ryan, the Wisconsin Republican who will take leadership of the House budget committee, said the GOP will rein in the overhaul through oversight hearings and cutting off money to implement the law, "but then again, the president has to sign those bills, so that is a challenge."

"You can't fully repeal and replace this law until you have a new president and a better Senate. And that's probably in 2013, but that's before the law fully kicks in, in 2014," Ryan said.

Meanwhile, Rand Paul, the tea party-backed winner in Kentucky's Senate race, said cuts to military spending and programs such as Social Security had to be considered, a break from Republican positions that both are sacrosanct. "We're coming. We're proud. We're strong. We're loud. And we're going to co-opt. And, in fact, I think we're already shaping the debate," he said of his fellow tea party candidates.

And Sen. Jim DeMint, R-S.C., who emerged as a leader of tea party-style candidates, said the GOP was to blame for its loss in Delaware's Senate contest between Republican Christine O'Donnell and Democrat Chris Coons. "Unfortunately, she was so maligned by Republicans, I don't think she ever had a chance," DeMint said of the candidate whom party leaders tried to block from the nomination by highlighting her previous statements on masturbation and evolution.

Pence and Paul appeared on ABC's "This Week." Van Hollen spoke to CNN's "State of the Union." Cantor and Ryan were interviewed on "Fox News Sunday" while McConnell and Clyburn appeared on CBS' "Face the Nation." DeMint spoke in NBC's "Meet the Press."